Between June 27 and 3 there was one coronavirus-related death in care homes in the Hampshire County Council area, and none in Portsmouth and Southampton, according to the latest figures from the Office for National Statistics (ONS).
This was a repeat of the previous week but a drop from two weeks prior when there were five deaths in the Hampshire council area.
It comes as prime minister Boris Johnson was criticised for suggesting care homes were partly to blame for the number of overall coronavirus deaths.
During an interview Mr Johnson said: 'We discovered too many care homes didn't really follow the procedures in the way that they could have but we're learning lessons the whole time.'
Downing Street has since declined to apologise for the comment.
Speaking at a virtual health and wellbeing meeting today, Portsmouth council's health boss, Councillor Matthew Winnington, said: 'It's a litany of blame shifting. I think that the response of the government in general was very poor.
'I think the response in our city has been amazing.
'They have tried to shift the blame from what was utter chaos. Day by day the guidance was changing and if we were one of those authorities that didn't pre-plan we would have been in an utter mess.'
Cllr Liz Fairhurst, Hampshire County Council’s health boss, added: 'Every death is a cause for sadness, but we do not believe this is a reflection of the quality of care provided by Hampshire’s care sector, or the infection control measures in place.
'Indeed the support the sector has provided is marked by its humanity, professionalism and the highest quality of care.
'We continue to support the sector to reduce transmission of the virus, though a variety of measures including help to access the requisite PPE, providing advice on issues such as staffing practice or how to isolate people safely, as well as practical help such as the delivery of infection control training.'
The south east regional secretary for union Unison, Steve Torrance, said: 'We all owe a debt of gratitude to the dedicated care staff who have worked so hard in difficult conditions to help get the outbreak in Hampshire’s care homes under control.
'The prime minister’s comments are unhelpful and the underfunding of social care shouldn’t be a surprise to him.'
The Hampshire County Council area has still seen the most care home deaths linked to Covid-19 since records began on April 10 with 388.
The total in Portsmouth is 37 and the total in Southampton is 56.
Some of the weekly figures increase in later data releases when more deaths from the period are notified to Care Quality Commission.